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Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian is self-adjoint; this issue is subtle for a particular category of factor orderings. We identify and parametrize a complete set of self-adjoint extensions and provide a canonical description of these extensions in terms of boundary conditions. Moreover, we use Trotter-type product formulae to construct path-integral representations of time evolution.
Keywords: factor ordering in quantum gravity; path integrals in quantum gravity; singularity avoidance in quantum gravity; quantization on a half-line. 
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     author = {John Haga and Rachel Lash Maitra},
     title = {Factor {Ordering} and {Path} {Integral} {Measure} for {Quantum} {Gravity} in~(1+1) {Dimensions}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a38/}
}
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John Haga; Rachel Lash Maitra. Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a38/

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